The Chicago Opera is setting prices for a subscription to next seasons performances and they've hired a consultant. The consultant has determined that the audience is composed of two types of customers. The first are "patrons", who are affluent and committed opera lovers. By studying past demand the consultant determines that the patron's demand is described by the equation Pp = 450 - .15Qp, where Pp is the price a patron must pay for a subscription and Qp are the number of patron subscriptions.
The other group of potential subscribers is "students", who are generally less affluent and less committed to opera. Their demand is given by Ps = 300 - .15Qs, where Ps is the price a student must pay for a subscription and Qs are the number of student subscriptions.
a) Imagine the opera has a capacity of 3000 seats and that all costs are fixed. If they can discriminate between the two groups, what is optimal price to charge to each group and how many tickets will each group buy?
b) If the opera can only seat 2000 people and can discriminate what is optimal price to charge to each group and how many tickets will each group buy?
c) If the opera has a capacity of 3000 but cannot discriminate (i.e., they must charge the same price to everyone). What is the optimal price?